Percolation in two-dimensional systems containing cyclic chains

Abstract

The structure of the system consisting of adsorbed cyclic polymer chains and solvent molecules was studied. Our main aim was to check how the percolation threshold in such a system was related to the percolation threshold obtained for a system of “ordinary” flexible linear chains, i.e. how the geometry of objects influenced the percolation threshold of regarded objects and solvent molecules. The macromolecules were represented as sequences of statistical segments restricted to a two-dimensional triangular lattice. The system was athermal and the excluded volume was the only potential introduced. The properties of the system were determined by means of the Monte Carlo method using the cooperative motion algorithm (CMA). The percolation thresholds and critical exponents were determined. It was shown that the percolation threshold of cyclic chains was considerably higher than that of linear chains and depends on the chain length less significantly then for linear polymers.